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Originally Posted by Legs
Well yes I have seen that theory presented. I would call it a theory not an explanation.
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The "theory" is that it's rational to base beliefs on the evidence. That's all it is.
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No one knows for sure what the true murder rate is.
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Whether or not that's true, it's simply not what I addressed. Let the true (population) murder rate be 10 times higher than the known (sample) murder rate, if that sufficiently appeals to your sense of hidden evil. The issue was whether there's any reason to believe the two rates would
change independently. As in your question: "How can we honestly say murdered children rates are dropping with such a huge unknown factor?"
On this question it's sufficient to point out that no other conclusion is rational
in the absence of special reason to regard sample rate changes as delusive relative to the population. You have no such reason, though -- or none that you will share. So, yes, if the sample murder rate is static, or drops in some statistically significant way, that's the best evidence one could have that the population rate is static or dropping too.